The New Sudoku Players' Forum

[jco]

Hi !
I am "puzzled" by the following puzzle from Mauricio (source: Sudopedia on "uniqueness clue cover")

Code: Select all

*-----------*
|...|...|...|
|...|...|..2|
|...|..1|...|
|---+---+---|
|..1|.3.|.4.|
|..5|6.7|3..|
|.3.|.2.|..8|
|---+---+---|
|..2|.6.|5..|
|65.|..8|9.4|
|9..|4..|..7|
*-----------*

.................2.....1.....1.3..4...56.73...3..2...8..2.6.5..65...89.49..4....7 ER = 8.4
Following the very short explanation given at the sudopedia site, one can make r1c9=1, solving the puzzle with singles.
From that site:

More dramatically, if a band contains just two clues in the arrangement shown (starred) below, then all of the unclued values are eliminated from two other cells. Note that although it is obvious that -@ in r2c3 implies r2c3=1, this placement is not shown because the elimination of 2 from r2c3 does not require any uniqueness assumption: we are applying the definition strictly.

Code: Select all

+-------------+-------------+-------------+
|   .   .   . |   .   .   . |   .   .  *1 |
|   .   .  -@ |   .   .   . |   .   .  -@ |
|   .   .  *2 |   .   .   . |   .   .   . |
+-------------+-------------+-------------+


These eliminations are available because only a few special types of band (in this case) can be covered by just two clues in any proper, single-solution, puzzle. Knowing the form that these special band types take, by computer searching, allows us to make the eliminations shown.

I may have misunderstood something. Is there (nowadays) a way (proof) to justify that placement using uniqueness but without "computer searching" ? I could not find a thread on this and Wecoc's List of Acronyms points only to Sudopedia.

Many thanks in advance!

[eleven]

If i remember right:
As it says above, all possible solution grids for puzzles with only 2 clues given in a band in different boxes and rows, do have this property (the band alone of course can have many other solutions, but for a unique puzzle solution without that property you would need another given in the band). That was found by exhaustive search.
But i cannot find a reference, when/where that was shown.

[StrmCkr]

reverse bug
by ruud

if i remember correctly covered the early proof and "UCC" yiddish version of "yuck" exhaustively searched unavoidable sets for reduced space to prove it somewhere just as we lost the original server.

[sultan vinegar 2]

Interesting; I had never seen this technique before. AUR, AUL, and BUG yes, but UCC no. Thank you for posting.

Could anyone help me with something that doesn't sit right about it with me? Take that puzzle by Mauricio from the first post. Suppose I am struggling with it, so you provide me with an extra given in the top band to make it easier. That doesn't change the solution, so that UCC constraint must apply regardless of the number of givens in the top band, mustn't it?

This type of constraint reminds me of something that I believe I read years' ago about a constraint to the number of relative position switches within a band for a given digit. Does anyone know to what I refer, and is this constraint covered on this forum?

[Serg]

Hi, sultan vinegar 2!

Could anyone help me with something that doesn't sit right about it with me? Take that puzzle by Mauricio from the first post. Suppose I am struggling with it, so you provide me with an extra given in the top band to make it easier. That doesn't change the solution, so that UCC constraint must apply regardless of the number of givens in the top band, mustn't it?

Suppose one is searching for valid puzzles for the following pattern:

Code: Select all

+-----+-----+-----+
|. . .|. . .|. . .|
|. . .|. . .|. . x|
|. . .|. . x|. . .|
+-----+-----+-----+
|x x x|x x x|x x x|
|x x x|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|x x x|x x x|x x x|
|x x x|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+

It turns out, the valid puzzles for this pattern do exist. Exhaustive search for this pattern shows some non-evident properties of those puzzles and their solutions.

Code: Select all

+-----+-----+-----+
|. . .|. . A|. . B|
|. . .|. . .|. . C|
|. . .|. . D|. . .|
+-----+-----+-----+
|x x x|x x x|x x x|
|x x x|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|x x x|x x x|x x x|
|x x x|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+

Valid puzzle's property: C must not be equal to D.
Valid puzzle solution's property: A always is equal to C, B always is equal to D.

So, "Valid puzzle solution's property" can be used as a Sudoku solving rule - "If Sudoku puzzle to be solved has 2 clues in some band (stack) occupying 2 different boxes and 2 different rows (columns), 2 minicolumns (minirows) of the solution grid, containing these clues, must contain "opposite" clue digits in order the puzzle can have a unique solution."

Serg